String Tension Calculator
The pitch of a plucked or bowed string is set by its tension, its vibrating length, and how heavy the string is per unit of length. Rearranging the classic vibrating-string equation lets you solve for the tension required to bring a string to a target pitch. Enter the note frequency in hertz, the scale (vibrating) length in metres, and the string's mass per unit length in kilograms per metre. This calculator returns the required tension in newtons, kilograms-force, and pounds-force so you can check it against an instrument's safe range.
String tension formula
T = mu * (2 * L * f)^2 (newtons)
wave speed v = 2 * L * f (m/s)
kilograms-force = T / 9.80665
pounds-force = T / 4.4482216153
L is the vibrating length in metres, mu is the linear mass density in kg/m, and f is the fundamental frequency in hertz. This is the standard formula for the fundamental mode of an ideal flexible string.
Working with string tension
- Heavier strings (larger mass per length) need more tension for the same pitch.
- A longer scale length raises tension for the same note and gauge.
- Total tension across all strings is what loads the instrument's neck and top.
- Always check the manufacturer's published safe tension range before stringing up.
- This model treats the string as perfectly flexible; real stiff strings read slightly sharp.
String tension: frequently asked questions
What is the vibrating string tension formula?
The fundamental frequency of a vibrating string is f = (1 / 2L) times the square root of T divided by mu, where L is the vibrating length, T is tension, and mu is the mass per unit length. Rearranged for tension: T = mu times (2 * L * f) squared. With length in metres, mu in kilograms per metre, and frequency in hertz, T comes out in newtons.
How do I find the mass per unit length of a string?
Weigh a known length of the string and divide its mass by that length, giving kilograms per metre. Manufacturers also publish a unit weight for each gauge, often in pounds per inch, which can be converted to kg per metre. Enter that value directly so no figure is assumed.
How do I find the target frequency for a note?
Use the equal-tempered frequency of the note you want. For example, standard A4 is 440 Hz and the open A string on a guitar (A2) is 110 Hz. Our note frequency tools convert any note name to its frequency in hertz, which you then enter here.
Why does the result also show kilograms-force?
String and instrument makers often think in kilograms-force or pounds, not newtons. Dividing the newton result by 9.80665 gives the equivalent kilograms-force, a more intuitive sense of how hard the string pulls on the instrument.
Sources and definitions
- The vibrating-string equation f = (1/2L) sqrt(T/mu) is a standard result of classical mechanics and acoustics; tension follows by algebraic rearrangement.
- The standard gravity constant 9.80665 m/s squared and the pound-force conversion (4.4482216153 N) are defined by the National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.